Algebra Geometry And Software Systems
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Algebra Geometry And Software Systems
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Author : Michael Joswig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Algebra Geometry And Software Systems written by Michael Joswig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
In many fields of modern mathematics specialised scientific software becomes increasingly important. Hence, tremendous effort is taken by numerous groups all over the world to develop appropriate solutions. This book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volume's other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general framework for modular systems.
Software For Algebraic Geometry
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Author : Michael E. Stillman
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-29
Software For Algebraic Geometry written by Michael E. Stillman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-29 with Mathematics categories.
Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop “Software for Algebraic Geometry” held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.
Geometric Algebra For Computer Science
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Author : Leo Dorst
language : en
Publisher: Elsevier
Release Date : 2010-07-26
Geometric Algebra For Computer Science written by Leo Dorst and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-26 with Computers categories.
Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing* Written by leaders in the field providing essential information on this new technique for 3D graphics* This full colour book includes a website with GAViewer, a program to experiment with GA
Ideals Varieties And Algorithms
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Author : David Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Ideals Varieties And Algorithms written by David Cox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
We wrote this book to introduce undergraduates to some interesting ideas in algebraic geometry and commutative algebra. Until recently, these topics involved a lot of abstract mathematics and were only taught in graduate school. But in the 1960's, Buchberger and Hironaka discovered new algorithms for manipulating systems of polynomial equations. Fueled by the development of computers fast enough to run these algorithms, the last two decades have seen a minor revolution in commutative algebra. The ability to compute efficiently with polynomial equations has made it possible to investigate complicated examples that would be impossible to do by hand, and has changed the practice of much research in algebraic geometry. This has also enhanced the importance of the subject for computer scientists and engineers, who have begun to use these techniques in a whole range of problems. It is our belief that the growing importance of these computational techniques warrants their introduction into the undergraduate (and graduate) mathematics curricu lum. Many undergraduates enjoy the concrete, almost nineteenth century, flavor that a computational emphasis brings to the subject. At the same time, one can do some substantial mathematics, including the Hilbert Basis Theorem, Elimination Theory and the Nullstellensatz. The mathematical prerequisites of the book are modest: the students should have had a course in linear algebra and a course where they learned how to do proofs. Examples of the latter sort of course include discrete math and abstract algebra.
Geometric And Algorithmic Aspects Of Computer Aided Design And Manufacturing
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Author : Ravi Janardan
language : en
Publisher: American Mathematical Soc.
Release Date :
Geometric And Algorithmic Aspects Of Computer Aided Design And Manufacturing written by Ravi Janardan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Computer-Aided Design and Manufacturing (CAD/CAM) is concerned with all aspects of the process of designing, prototyping, manufacturing, inspecting, and maintaining complex geometric objects under computer control. As such, there is a natural synergy between this field and Computational Geometry (CG), which involves the design, analysis, implementation, and testing of efficient algorithms and data representation techniques for geometric entities such as points, polygons, polyhedra, curves, and surfaces. The DIMACS Center (Piscataway, NJ) sponsored a workshop to further promote the interaction between these two fields. Attendees from academia, research laboratories, and industry took part in the invited talks, contributed presentations, and informal discussions. This volume is an outgrowth of that meeting.
Future Curricular Trends In School Algebra And Geometry
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Author : Zalman Usiskin
language : en
Publisher: IAP
Release Date : 2010-06-01
Future Curricular Trends In School Algebra And Geometry written by Zalman Usiskin and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-01 with Education categories.
This volume contains papers from the Second International Curriculum Conference sponsored by the Center for the Study of Mathematics Curriculum (CSMC). The intended audience includes policy makers, curriculum developers, researchers, teachers, teacher trainers, and anyone else interested in school mathematics curricula.
Mathematical Software
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Author : Arjeh M. Cohen
language : en
Publisher: World Scientific
Release Date : 2002
Mathematical Software written by Arjeh M. Cohen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Annotation The advent of mathematical software has been one of the most important events in mathematics. Mathematical software systems are used to construct examples, to prove theorems, and to find new mathematical phenomena. On the other hand, mathematical research often motivates developments of new algorithms and new systems. Mathematical software systems rely on the cooperation of mathematicians, designers of algorithms, and mathematical programmers. This book is aimed at software developers in mathematics and programming mathematicians, but it also provides opportunities to discuss the topics with mathematicians.
Computer Algebra In Scientific Computing
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Author : Vladimir P. Gerdt
language : en
Publisher: Springer
Release Date : 2016-09-08
Computer Algebra In Scientific Computing written by Vladimir P. Gerdt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-08 with Computers categories.
This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.
Topics In Algebraic Geometry And Geometric Modeling
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Author : Ron Goldman
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Topics In Algebraic Geometry And Geometric Modeling written by Ron Goldman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of mechanical components and assemblies for industrial design and manufacture. The NSF sponsored the four-day ''Vilnius Workshop on Algebraic Geometry and Geometric Modeling'', which brought together some of the top experts in the two research communities to examine a wide range of topics of interest to both fields. This volume is an outgrowth of that workshop. Included are surveys, tutorials, and research papers. In addition, the editors have included a translation of Minding's 1841 paper, ''On the determination of the degree of an equations obtained by elimination'', which foreshadows the modern application of mixed volumes in algebraic geometry. The volume is suitable for mathematicians, computer scientists, and engineers interested in applications of algebraic geometry to geometric modeling.
Mathematical Software Icms 2014
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Author : Hoon Hong
language : en
Publisher: Springer
Release Date : 2014-08-01
Mathematical Software Icms 2014 written by Hoon Hong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Computers categories.
This book constitutes the proceedings of the 4th International Conference on Mathematical Software, ICMS 2014, held in Seoul, South Korea, in August 2014. The 108 papers included in this volume were carefully reviewed and selected from 150 submissions. The papers are organized in topical sections named: invited; exploration; group; coding; topology; algebraic; geometry; surfaces; reasoning; special; Groebner; triangular; parametric; interfaces and general.